EIS measurements for characterization of muscular tissue by means of equivalent electrical parameters

Measurement 58 (2014) 476–482

Contents lists available at ScienceDirect

Measurement journal homepage: www.elsevier.com/locate/measurement

EIS measurements for characterization of muscular tissue by means of equivalent electrical parameters Fabrizio Clemente a,⇑, Maria Romano b,c, Paolo Bifulco b,c, Mario Cesarelli b,c a

Istituto di Ingegneria Biomedica/Istituto di Biostrutture e Bioimmagini, Consiglio Nazionale delle Ricerche, Monterotondo S., Roma, Italy DIETI, Università degli Studi di Napoli ‘‘Federico II’’, Napoli, Italy c Interuniversity Centre of Bioengineering of the Human Neuromusculoskeletal System b

a r t i c l e

i n f o

Article history: Received 16 April 2014 Received in revised form 31 July 2014 Accepted 5 September 2014 Available online 16 September 2014 Keywords: Biological measurement Electrical impedance spectroscopy Muscle Electrical models of biological tissue Isometric contraction

a b s t r a c t The objective of this work was to study the use of electrical impedance spectroscopy (EIS) measurement to characterize muscle electrical properties in different conditions. In vivo EIS measurements were carried out in the range 1–60 kHz on 32 forearm flexor muscles of healthy volunteers. Each subject underwent to a protocol consisting of three trials: rest condition, isometric contraction, 4 min relaxation. Measured data were fitted with Cole–Cole equivalent electrical circuit using the complex nonlinear least square method. Finally, the relative variations from the steady state of the electrical parameters of the equivalent electrical circuit were estimated. Results obtained are in agreement with the hypothesis that, in the frequency range considered, the current preferentially flows through the extracellular fluid, being the component of intracellular resistance negligible. Among circuital parameters, in fact, the relative variations from steady state of R0 changed highly significant (p < 0.001) both during contraction and after 4 min relaxation. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction The human body, like any conductive material, provides some impedance to the passage of electric current. The measure of this impedance is a field of engineering research, already employed also in medical practice. This technique is applied to muscle tissue, sometimes named Electrical Impedance Myography (EIM), is a poorly invasive tool for neuromuscular evaluation. Generally speaking in EIM an alternating current is injected via surface electrodes and the resulting voltage drop over a selected muscle or muscle group is measured [1–5]. Many applications concerning analysis of muscular tissue can be found in literature, in particular with the issue to characterize different physiological or pathological conditions [1–3,5]. As the ⇑ Corresponding author. Tel.: +39 0690672493; fax: +39 0690672692. E-mail address: [email protected] (F. Clemente). http://dx.doi.org/10.1016/j.measurement.2014.09.013 0263-2241/Ó 2014 Elsevier Ltd. All rights reserved.

impedance of biological tissue is frequency dependent, important information can also be obtained measuring tissue in a range of frequencies; this technique is generally referred to as electrical impedance spectroscopy (EIS) [5,6]. EIS measures have already produced interesting results in different clinical applications [1,7–10]. For example, the method has been successfully employed for characterizing in vivo changes in skin electrical properties due to drug delivery or for monitoring the osteointegration process of metallic implants for auditory recovery; this technique has been used also for studying changes in electrical properties of muscular tissue at low levels of contraction or for testing health condition of muscles in elderly subjects. However, additional investigations are needed to better highlight complex mechanisms involved in tissue’s intrinsic changes [7–9]. Muscular impedance depends in fact on different factors, such as biochemical changes, structure and geometry of the muscle itself, direction of

F. Clemente et al. / Measurement 58 (2014) 476–482

the applied current, kind of electrodes used and inter electrode distance [9,10]. Moreover there is a lack of standards in measurement parameters, lay out and protocol [10–12]. In biomedical engineering, it is common to model systems and particular electrical measurement of biological tissues by means of equivalent electrical circuits which provide a simplified description of the properties of the measured organs [6,13,14]. An opportune choice of the model makes possible to correlate the circuit elements to underlying physical and physiological processes [7,13]. Muscular tissue, such as any other biological tissue, is formed by cells whose structure can be represented by considering extra cellular fluids (blood and interstitial fluid), cell membrane and intra cellular components [14]. From the electrical point of view, intra and extracellular media can be considered as a liquid electrolyte (represented by a resistive component) and the cell membrane, being characterized by a double layer of lipids, behaves as a capacitor [6,7]. Thus it is possible to study the modifications in muscular tissue, related to different conditions, analyzing the correspondent changes in the equivalent electrical parameters. Recently, it has been demonstrated that those changes are large enough to be considered as sufficiently sensitive, reproducible and hence appropriate for clinical use [11,12]. However, on the basis of our knowledge, except some isolated case [4,12,13], not many research works there exist specifically concerning the relationship between electrical circuits and muscle tissue. The objective of this work was to study the variation of muscle electrical properties in three different muscle conditions, rest, sustained contraction and phase after contraction; of which the last two conditions are poorly studied in literature. To this aim, an equivalent electrical model was adopted to analyze the forearm flexor muscles and in vivo EIS measurements were employed to estimate changes in the equivalent electrical parameters of the tissue impedance in order to evaluate their sensibility to the variation of the muscular state. The paper in the following considers different aspects of the study. The methods section includes impedance measurement background, instrumentation and lay out and protocol for muscular tissue measurement; moreover this section describes the used equivalent electrical model, the fitting and data analysis procedure. The result section shows raw data analysis according to the previously described approach which are examined in Section 4. 2. Method 2.1. Impedance measurement for biological tissue characterization For this study, the logical scheme represented in Fig. 1 was adopted. This scheme follows the general approach employed to define the procedures to test new in vivo measurement methods [7]. In this application the impedance of the tissue under measurement was evaluated by means of the equation:

Z¼

jVj jðhV hI Þ e jIj

477

where |V|, hV and |I|, hI represent, respectively, modulus and phase of the acquired sinusoidal voltage and of the injected current signal. In order to implement the impedance measure, an appropriate measurement system must be designed and utilized [11,15].

2.2. Measurement system 2.2.1. Hardware The prototyped proof demonstrator, based on a batterypowered notebook PC implemented with an AD/DA board and an analog interface, has been described elsewhere [7,16,17]. It was used, in a clinical tool, for EIS measurements of transcutaneous implants during the osseointegration process [17] and for a preliminary evaluation of muscle tissue [11,16]. The digital I/O board was a PCMCI DAQCard-6062E (National Instrument™, Austin, Texas), with a two DACs and 16-channels ADC, all ones with a 12-bits resolution. One of the DACs was used to generate the low voltage sinusoidal stimulus [18]. The analog output of the DAC was amplified by a high-accuracy instrumentation amplifier and applied between the A+/A– electrodes. The current value was measured by a transimpedance amplifier. The tissue drop voltage was gathered between the V+/V– electrodes by means of another high-accuracy differential amplifier (chosen to guarantee high noise immunity and common-mode rejection). The output voltages of the differential amplifiers were sampled by the two channels of the ADC and processed by the software (described in the following sub-section) for impedance evaluation.

2.2.2. Software The software, derived from [15] and detailed in [11], was designed in LabVIEW environment (National Instruments). It was developed for (i) managing the acquisition board; (ii) setting and controlling the stimulus, by means of a loop procedure, in order to maintain constant the voltage drop, at a value here called Vp, over the portion of tissue under measurement (in accordance with the typical procedure employed in EIS measurements [18]); (iii) checking the amplitude of current stimulus (kept within safety levels) [8,17]; (iv) implementing a sine-fitting technique [20], to reduce the influence of noise in the final impedance computation; (v) averaging modulus and phase of five measurements for impedance evaluation and (vi) generating and saving an ASCII file with all the impedance parameters. All the operations can be easily executed by the operator using a front panel interface developed in LabVIEW, which allows also to see, in real time, frequency-courses of modulus and phase of the measured impedance.

2.3. Measurement lay out EIS measurements were carried out by employing tetra polar measurements, since it is known that the use of four electrodes can help to isolate an area of interest and, mainly, to reduce the effects of electrode polarization [6].

478

F. Clemente et al. / Measurement 58 (2014) 476–482

Fig. 1. Measurement procedure for muscular tissue characterization.

As in [1,5], surface electrodes (here Biatrodes electrodes, Akern, Pontassieve, FI [11,16]) specifically designed for bioimpedance measurements were used. Measurements were performed on the forearm flexor muscles. Before measurement, each subject underwent to an accurate skin cleaning of the tissue under test by means of a slightly abrasive towel (Electrode Skin Prep PadsDynarex), in order to eliminate sebum and dead cells. In order to standardize the measurements, great attention was posed to subject posture and electrodes positioning. All the subjects seated with the arm on a desk and the palm turned upward. The forearm formed with the arm an angle of about 150°. Electrodes were placed aligned on the forearm; the current electrodes on the elbow and on the wrist and voltage ones on the muscle belly (the first at 4 cm from the elbow) with an inter-distance of 6 cm (Fig. 2). 2.4. Protocol [11] 2.4.1. Parameters for muscular tissue measurement The measurement frequency range was 1–60 kHz. The lower limit eliminates EMG surface signal [19], the upper limit is to elicit a part of b region [14] in order to probe both properties of cell and cell suspension [21]. The linear frequency sweep was of 10 points to limit the time length of the test and hence to avoid subjects’ fatigue [11,19,22] (each test takes about 1 min).

Fig. 2. Pratical example of electrodes positioning.

2.4.2. Subjects and measurement protocol Sixteen healthy volunteers (11 men and 5 women, age 27.5 ± 7.1), not affected by any neurological or musculoskeletal disorder, not trained and in good general health, were involved in the study. Each subject underwent to a test protocol consisting of three trials:  in rest condition (steady state),  at 60–70% of the maximum effort (sustained contraction),  4 min after contraction. As no difference was observed between results obtained by dominant and not dominant arm, as was confirmed from a paired t-test (t-value = 0.22 – p-value = 0.82), for each subject the protocol was performed for both forearms, so that instead of 16 subjects, 32 tests are considered in the following. To execute the contraction trial, all subjects were asked to exert isometric gripping force against a hand dynamometer. The effort percentage was measured by means of Calibrated KERN HGD dynamometer (trials in which force values were out of this range were excluded from the study) [11]. The trial was not executed at the maximum effort to avoid the subject’s inability to maintain the contraction for the necessary time but at a percentage of its maximum able to induce clear muscular changes [19,22]. 2.5. Equivalent electrical model Biological tissues are not homogeneous media, to explain their behavior has been hypothesized a distribution of relaxation time constants and many relaxation functions have been proposed to describe that situation. Many equivalent electrical circuits have been proposed for EIS. Among them, we choose, as starting point, the model introduced by Cole–Cole (1941), shown in Fig. 3, because it is the most widely used and is largely adopted for biological tissues too [7,23–25].

F. Clemente et al. / Measurement 58 (2014) 476–482

Cole–Cole model is expressed by the formula [6,7]:

Z tissue ¼ Z 1 þ

ðZ 0  Z 1 Þ 1 þ ð jxTÞ

d

2.6. Fitting software

ð1Þ

where Z1 represents the electrical impedance at high frequency, Z0 at low frequency, x = 2pf ( f is the frequency), T is the circuit time constant, and d (0 6 d 6 1) is a dimensionless empirical parameter characteristic of the distribution of the relaxation times of the various structures forming the tissue [6,23]. When this approach is employed, since biological tissues show a very complex behavior which cannot be described using only simple, real electrical elements neither a combination of RC loops [6], the ‘‘constant phase element’’ (CPE), i.e. a further circuit element called Zcpe [6,13] (element represented as a box in Fig. 3) that produces a phase shift nearly constant, is useful and accepted elsewhere [6,7,13,23] to fit EIS data in biological tissues measurements. The CPE has the following analytical expression [6]:

Z cpe ¼ Að jxÞ

d

ð2Þ

where A is a constant and represents the amplitude of the impedance pseudo-capacitive. It is important to put in evidence that Zcpe is not a real component, but a pseudocapacity, without physical reality, used only as a means to express some experimental results. From the formula 2, it can be deduced that when d = 1, Zcpe is a pure capacity, while when d = 0, it is a pure resistance. Biological tissues, at very-high and very-low frequencies are commonly represented as pure resistors [6,7], thus the impedances Z1 and Z0 in the Eq. (1) can be replaced by the ideal resistors R1 and R0:

Z tissue ¼ R1 þ

ðR0  R1 Þ 1 þ ð jxTÞ

d

ð3Þ

Combining formulas (2) and (3), it is possible to compute the parameter A:

A ¼ ðR0  R1 Þ

1 Td

479

ð4Þ

Therefore the tissue under examination can be characterized through 4 direct parameters (R1, R0, d, T, A) and one derived parameter (R0  R1) to be correlated to biological components [6,7].

Different fitting methods there exist to obtain the values of the physical quantities of interest from the measured impedance data. Nowadays, the preferred one is the complex nonlinear least square (CNLS) fit method, already known in literature and used in biological applications [6,7], which has as an important advantage the possibility of fitting all the data simultaneously [26]. Of course, for performing the CNLS method a proper software is necessary. Here, the LEVMW software, version 8.11 for Windows™ was used, considering that it has been already largely employed for industrial and scientific application of EIS [27]. This software, widely described in LEVMW manual [28], can be employed to analyze the electrochemical, dielectric and conductive properties of a given system. It allows setting a specific electric model to fit the experimental input data, analyze the response of the model and solve the problem of estimating the distribution of relaxation times. Software’s strength is that the operator can select a circuit fitting, modify it conveniently, and therefore set the various circuit elements that compose it very easily. 2.7. Data analysis Once recorded impedance values during test protocol, values of all parameters (R1, R0  R1, d, T, A) of the equivalent electrical model considered were estimated using the LEVM software. In addition, also the values of R0 were estimated since it is directly linked to the extra-cellular resistance [7,13,14]. In this study, according to a previous one [11], the steady state was considered as a reference and for the other conditions (contraction and 4 min after) the relative variations of all electrical parameters were evaluated. To indicate computed data, the following symbols were used as subscripts: C|S, relative variation of the parameter X computed in the trial of contraction (C) respect to the value computed S in steady state (S), X CjS ¼ X CXX . S A|S, relative variation the a parameter X computed 4 min after contraction (A) respect to the value computed S . in steady state (S), X AjS ¼ X AXX S Results of statistical analysis and related figures were obtained by employing the software Minitab 16. Then, for each parameter, the Kolmogorov–Smirnov test was applied to verify the normality of the data distributions and the t-test was applied to the two pairs of data classes (contraction respect to steady state and 4 min after respect to steady state) for verifying if relative variations are significantly different from the null value, corresponding to the steady state, and between them (the test was considered significant if p < 0.01). 3. Results

Fig. 3. Electrical circuit corresponding to the Cole–Cole equation and chosen for this research work.

To evaluate if the target parameters vary or not in the different muscular states mean and SD of relative variations of the electrical parameters are reported in Table 1.

480

F. Clemente et al. / Measurement 58 (2014) 476–482

The Kolmogorov–Smirnov test demonstrated the data normality of the relative variations but only the parameters R0  R/ and R0 showed data classes significantly separated (as confirmed by the t-test, values reported in Table 2).

Table 2 Results of the t-test.

4. Discussion Impedance measurements have been proposed from a long time to study skeletal muscle, the first research works date back to the late 50s and early 60s [5,29,30] and they are still employed as a noninvasive tool for assessing different physiological or illness states [4,8,10,11,17]. However, analysis of the muscular status is a complex topic, since various and numerous physiological and psychological phenomena contribute to the muscle condition so that a set of techniques may be necessary for its characterization [31]. EIS measurements proved their usefulness in a variety of research and clinical applications [10,18]. Tissue analysis through EIS measurements can be performed by simple visual analysis of Bode and/or Nyquist plots or trying to obtain parameters useful in clinical setting. In a previous work [11], a concise index was computed to characterize muscle states. However that index has not a clear physiological correlate. In this work, a procedure for in vivo EIS measurements described elsewhere was employed [11], in order to provide preliminary results of muscle tissue characterization by fitting data to electrical networks [16]. To this aim, by literature, was employed an equivalent electrical model of biological tissues, obtained starting from the known model of Cole–Cole. After the definition of measurement lay out and protocol, in vivo tests were realized to characterize forearm flexors in three different conditions, steady state, contraction, some minutes after contraction, by means of the electrical parameters of the selected circuit. In particular, by using LEVMW software, were estimated the relative variations of the electrical parameters R1, R0  R1, d, T, A e R0, computed in sustained contraction and 4 min after, considering the steady state as reference.

Table 1 Values of the electrical parameters. Parameter

Mean ± SD

R1C|S R1A|S R0  R1C|S R0  R1A|S dC|S dA|S TC|S TA|S AC|S AA|S R0C|S R0A|S

0.093 ± 0.064 0.044 ± 0.078 0.091 ± 0.076 0.067 ± 0.054 0.032 ± 0.034 0.048 ± 0.026 0.577 ± 0.885 0.212 ± 0.578 1.296 ± 23.074 0.902 ± 3.581 0.049 ± 0.002 0.022 ± 0.001

Obtained results are shown as mean ± standard deviation.

** ***

Hypothesis

Significance level

R1C|S – R1S|S R1A|S – R1S|S R1A|S – R1C|S

p < 0.046 p < 0.375 p < 0.464

R0  R1C|S – R0  R1S|S R0  R1A|S – R0  R1S|S R0  R1A|S – R0  R1C|S

p < 0.071 p < 0.111 p < 0.016

dC|S – dS|S dA|S – dS|S dA|S – dS|S

p < 0.331 p < 0.101 p < 0.714

TC|S – TS|S TA|S – TS|S TA|S – TC|S

p < 0.002** p < 0.124 p < 0.094

AC|S – AS|S AA|S – AS|S AA|S – AC|S

p < 0.137 p < 0.011 p < 0.668

R0C|S – R0S|S R0A|S – R0S|S R0A|S – R0C|S

p < 1.146 E07*** p < 0.001*** p < 3.643 E10***

Statistically very significant (p < 0.01). Statistically highly significant (p < 0.001).

Before discussing results, it should be noted that measurements were obtained considering the frequency range 1–60 kHz; as reported in literature concerning dielectric dispersion in biological tissues [14,21], this interval corresponds to a part of the b band (from 103 to <107 Hz) in the diagram of the permittivity and conductivity of tissues. For these frequencies, the conductivity remains very low while the permittivity begins to decrease [13], but it is still very high. It may think therefore that the current preferentially flows through the extracellular matrix and does not penetrate through the cell membrane [14,21]. In this circumstance, the component of intracellular resistance should be negligible and the methodology should highlight more easily modifications in extracellular resistance and, in case, in Zcpe. Results obtained here are in agreement with this hypothesis, in fact, among circuital parameters, only the variations of the parameter R0 showed changes statistically significant (p < 0.001, Fig. 4, Table 2) from one muscular state to another. The very significant increment of R0 in contraction state puts in evidence the impediment to blood flow due to mechanical compression of vessels into the muscle whereas its decrement after contraction could be due to the subsequent increase of muscle perfusion [14,32]. Besides, another hypothesis to justify the decrease of R0 after the contraction could be a general state of swelling characterizing a strained muscle [14] due to the sustained isometric contraction. It can be observed that also T had a significant change at least in contraction state (Fig. 5). This can represent an increase of capacitance on the measured muscular volume which is area dependant [30]. As in contraction the muscle increases its transversal area, the total measured capacitance increases.

F. Clemente et al. / Measurement 58 (2014) 476–482

481

Acknowledgments This paper was realized in the framework of projects: QUAM – Quantitative Assessment of Muscle Treatments, Conference of Italian University Rectors (CRUI) and Agency for foreign promotion and internationalization of Italian firms (ICE) (approved project n. 230/2010). Methods and devices for metallic prosthesis osteointegration diagnosis, Curiosity Driven Research (RSTL.045.005), National Research Council of Italy (CNR). References

Fig. 4. Boxplot of estimated relative variations for the parameter R0. The symbol ⁄ represents an outlier.

Fig. 5. Boxplot of estimated relative variations for parameter T. The symbol ⁄ represents outliers.

5. Conclusion The measurement of impedance of biological tissues can provide useful information about tissue changes which occur in some physiological and/or pathological conditions. To get reliable information about processes involved in these changes, it is possible to adopt equivalent electrical circuits of the tissue or organ measured, even if circuits are only models and have some limitations (for example according to literature [6,14,18] are not unique). In this work, the Cole–Cole model, a representation largely used for tissue modeling [7,13,23], has been proposed to study the relative variations of electrical parameters in forearm muscle EIS measurements in two conditions not yet considered in literature, sustained contraction and state reached 4 min after it, with respect to the rest condition considered as reference. Obtained results highlighted that, in physiological conditions, the employed protocol induces the greater modifications in the extracellular resistance which can be effectively monitored through the analysis of variations in equivalent electrical parameters.

[1] R. Aaron, G.J. Esper, C.A. Shiffman, K. Bradonjic, K.S. Lee, S.B. Rutkove, Effects of age on muscle as measured by electrical impedance myography, Physiol. Meas. 27 (2006) 953–959. [2] O.T. Ogunnika, M. Scharfstein, R.C. Cooper, H. Ma, J.L. Dawson, S.B. Rutkove, A handheld electrical impedance myography probe for the assessment of neuromuscular disease, in: 30th Annual International IEEE EMBS Conference 2008, Vancouver, British Columbia, Canada. [3] M. Jafarpoor, A.J. Spieker, J. Li, M. Sung, B.T. Darras, S.B. Rutkove, Assessing electrical impedance alterations in spinal muscular atrophy via the finite element method, in: 33rd Annual International conference of the IEEE EMBS 2011, Boston, Massachusetts USA. [4] C.A. Shiffman, R. Aaron, S. Rutkove, Electrical impedance of muscle during isometric contraction, Physiol. Meas. 24 (1) (2003) 213–234. [5] S.B. Rutkove, Electrical impedance myography: background, current state, and future directions, Muscle Nerve 40 (2009) 936–946. [6] B. Rigaud, J.P. Morucci, N. Chauveau, Bioelectrical impedance techniques in medicine. Part I: bioimpedance measurement. Second section: impedance spectrometry, Biomed. Eng. 24 (4–6) (1996) 257–351. [7] F. Clemente, P. Arpaia, C. Manna, Characterization of human skin impedance after electrical treatment for transdermal drug delivery, Measurement 2013 (46) (2013) 3494–3501. [8] F. Clemente, M. Costa, S. Monini, M. Barbara, Monitoring of fixture osteointegration after BAHA implantation, Audiol. Neurootol. 16 (3) (2010) 158–163. [9] S.B. Rutkove, R.A. Partida, G.J. Esper, A. Aaron, C.A. Shiffman, Electrode position and size in electrical impedance myography, Clin. Neurophysiol. 116 (2005) 290–299. [10] T. Zagar, D. Krizaj, Multivariate analysis of electrical impedance spectra for relaxed and contracted skeletal muscle, Physiol. Meas. 29 (6) (2008) S365–S372. [11] F. Clemente, M. Romano, P. Bifulco, M. Cesarelli, Study of muscular tissue in different physiological conditions using electrical impedance spectroscopy measurements, Biocybernet. Biomed. Eng. 34 (2014) 4–9. [12] C.A. Shiffman, S.B. Rutkove, Circuit modeling of the electrical impedance: I. Neuromuscular disease, Physiol. Meas. 34 (2013) 203–221. [13] M.E. Valentinuzzi, Bioelectrical impedance techniques in medicine. Part I: bioimpedance measurement. First section: general concepts, Biomed. Eng. 24 (4–6) (1996) 223–255. [14] Congo Tak-Shing Ching, Yueh-Chi Chen, Li-Hua Lu, Peiyuan F. Hsieh, Chin-Sung Hsiao, Tai-Ping Sun, Hsiu-Li Shieh, Kang-Ming Chang, Characterization of the muscle electrical properties in low back pain patients by electrical impedance myography, PLoS One 8 (4) (2013). [15] P. Arpaia, F. Clemente, C. Romanucci, An instrument for prosthesis osseointegration assessment by electrochemical impedance spectrum measurement, Measurement 41 (9) (2008) 1040–1044. [16] F. Clemente, M. Cesarelli, P. Bifulco, Electrical impedance spectral measurements of muscular tissue in different physiological condition, in: IEEE International Symposium on Medical Measurements and Applications Proceedings (MeMeA) 2012, pp. 1–4. [17] P. Arpaia, F. Clemente, C. Romanucci, In-vivo test procedure and instrument characterization for EIS-based diagnosis of prosthesis osseointegration, in: Proceedings of IEEE IMTC 2007, pp. 1–6. [18] P. Arpaia, F. Clemente, A. Zanesco, Low-invasive diagnosis of metallic prosthesis osseointegration by electrical impedance spectroscopy, IEEE Trans. Instrum. Meas. 56 (3) (2007) 784–789. [19] R. Merletti, P. Parker, Electromyography. Physiology, Engineering, and Noninvasive Applications, IEEE Press Engineering in Medicine and Biology Society, A John Wiley & Sons, Inc., Publication, 2004. Chapters 1, 4, 9.

482

F. Clemente et al. / Measurement 58 (2014) 476–482

[20] P.M. Ramos, M. Fonseca da Silva, A Cruz Serra, Low frequency impedance measurement using sine-fitting, Measurement 35 (1) (2004) 89–96. [21] W.D. Gregory, J.J. Marx, C.W. Gregory, W.M. Mikkelson, J.A. Tjoe, J. Shell, The Cole relaxation frequency as a parameter to identify cancer in breast tissue, Med. Phys. 39 (7) (2012). [22] M. Cesarelli, F. Clemente, M. Bracale, A very fast fourier transform algorithm to process biomedical signals using a PC-DOS personal computer, J. Biomed. Eng. 12 (6) (1990) 527–530. [23] L.C. Ward, T. Essex, B.H. Cornish, Determination of Cole parameters in multiple frequency bioelectrical impedance analysis using only the measurement of impedances, Physiol. Meas. 27 (2006) 839–850. [24] E.T. McAdams, J. Jossinet, Problems in equivalent circuit modelling of the electrical properties of biological tissues, Bioelectrochem. Bioenerg. 40 (1996) 147–152. [25] A.H. Lackermeier, E.T. McAdams, G.P. Moss, A.D. Woolfson, In vivo ac impedance spectroscopy of human skin, Ann. N. Y. Acad. Sci. 873 (1999) 197–213.

[26] J.R. Macdonald, et al., Impedance Spectroscopy. Theory, Experiment, and Applications, second ed., in: E. Barsoukov, J. Ross Macdonald (Eds.), John Wiley & Sons Inc., 2005. [27] http://www.jrossmacdonald.com/levminfo.html, (accessed July, 2014). [28] J.R. Macdonald, LEVMW Manual, www.jrossmacdonald.com/ levminfo, 2011. [29] P. Fatt, An analysis of the transverse electrical impedance of striated muscle, Proc. R. Soc. Lond. B Biol. Sci. 159 (1964) 606–651. [30] G. Falk, P. Fatt, Linear electrical properties of striated muscle fibres observed with intracellular electrodes, Proc. Roy. Soc. London, Ser. B Biol. Sci. 160 (1964) 69–123. [31] J.V. Basmajian, C.J. De Luca, Muscle fatigue and time-dependent parameters of the surface EMG signal, Muscle Alive, Williams & Wilkins, fifth ed., Cap. 8. [32] M.E. Tschakovsky, D.D. Sheriff, Immediate exercise hyperemia: contributions of the muscle pump vs. rapid vasodilation, J. Appl. Physiol. 97 (2004) 739–747.